Kinetic energy generation in heat engines and heat pumps: the relationship between surface pressure, temperature and circulation cell size

The pattern and size of the Earth’s atmospheric circulation cells determine regional climates and challenge theorists. Here the authors present a theoretical framework that relates the size of meridional cells to the kinetic energy generation within them. Circulation cells are considered as heat engines (or heat pumps) driven by surface gradients of pressure and temperature. This approach allows an analytical assessment of kinetic energy generation in the meridional cells from the known values of surface pressure and temperature differences across the cell, (Formula presented.) and (Formula presented.). Two major patterns emerge. First, the authors find that kinetic energy generation in the upper and lower atmosphere respond in contrasting ways to surface temperature: with growing (Formula presented.), kinetic energy generation increases in the upper atmosphere but declines in the lower. A requirement that kinetic energy generation must be positive in the lower atmosphere can limit the poleward cell extension of the Hadley cells via a relationship between (Formula presented.) and (Formula presented.). The limited extent of the Hadley cells necessitates the appearance of heat pumps (Ferrel cells)–circulation cells with negative work output. These cells consume the positive work output of the Hadley cells (heat engines) and can in theory drive the global efficiency of an axisymmetric atmospheric circulation down to zero. Second, the authors show that, within a cell, kinetic energy generation is largely determined by (Formula presented.) in the upper atmosphere, and by (Formula presented.) in the lower. By absolute magnitude, the temperature contribution is about 10 times larger. However, since the heat pumps act as sinks of kinetic energy in the upper atmosphere, the net kinetic energy generation in the upper atmosphere, as well as the net impact of surface temperature, is reduced. The authors use NCAR/NCEP and MERRA data to verify the obtained theoretical relationships. These observations confirm considerable cancellation between the temperature-related sources and sinks of kinetic energy in the upper atmosphere. Both the theoretical approach and observations highlight a major contribution from surface pressure gradients, rather than temperature, in the kinetic energy budget of meridional circulation. The findings urge increased attention to surface pressure gradients as determinants of the meridional circulation patterns.